1 Data preparation

1.1 Outline

  • Load scripts: loads libraries and useful scripts used in the analyses; all .R files contained in scripts at the root of the factory are automatically loaded

  • Load data: imports datasets, and may contain some ad hoc changes to the data such as specific data cleaning (not used in other reports), new variables used in the analyses, etc.

1.2 Load packages


library(reportfactory)
library(here)
library(rio) 
library(tidyverse)
library(incidence)
library(distcrete)
library(epitrix)
library(earlyR)
library(projections)
library(linelist)
library(remotes)
library(janitor)
library(kableExtra)
library(DT)
library(cyphr)
library(chngpt)
library(lubridate)
library(ggpubr)
library(ggnewscale)

1.3 Load scripts

These scripts will load:

  • all scripts stored as .R files inside /scripts/
  • all scripts stored as .R files inside /src/

These scripts also contain routines to access the latest clean encrypted data (see next section).


reportfactory::rfh_load_scripts()

1.4 Load clean data

We import the latest NHS pathways data:


x <- import_pathways() %>%
  as_tibble()
x
## # A tibble: 150,688 x 11
##    site_type date       sex   age   ccg_code ccg_name count postcode nhs_region
##    <chr>     <date>     <chr> <chr> <chr>    <chr>    <int> <chr>    <chr>     
##  1 111       2020-03-18 fema… 0-18  e380000… nhs_bar…    35 rm13ae   London    
##  2 111       2020-03-18 fema… 0-18  e380000… nhs_bed…    27 mk454hr  East of E…
##  3 111       2020-03-18 fema… 0-18  e380000… nhs_bla…     9 bb12fd   North West
##  4 111       2020-03-18 fema… 0-18  e380000… nhs_bro…    11 br33ql   London    
##  5 111       2020-03-18 fema… 0-18  e380000… nhs_can…     9 ws111jp  Midlands  
##  6 111       2020-03-18 fema… 0-18  e380000… nhs_cit…    12 n15lz    London    
##  7 111       2020-03-18 fema… 0-18  e380000… nhs_enf…     7 en40dy   London    
##  8 111       2020-03-18 fema… 0-18  e380000… nhs_ham…     6 dl62uu   North Eas…
##  9 111       2020-03-18 fema… 0-18  e380000… nhs_har…    24 ts232la  North Eas…
## 10 111       2020-03-18 fema… 0-18  e380000… nhs_kin…     6 kt11eu   London    
## # … with 150,678 more rows, and 2 more variables: day <int>, weekday <fct>

We also import demographics data for NHS regions in England, used later in our analysis:


path <- here::here("data", "csv", "nhs_region_population_2018.csv")
nhs_region_pop <- rio::import(path) %>%
  mutate(nhs_region = str_to_title(gsub("_"," ",nhs_region)))

nhs_region_pop$nhs_region <- gsub(" Of ", " of ", nhs_region_pop$nhs_region)
nhs_region_pop$nhs_region <- gsub(" And ", " and ", nhs_region_pop$nhs_region)
nhs_region_pop
##                  nhs_region variable      value
## 1                North West     0-18 0.22538599
## 2  North East and Yorkshire     0-18 0.21876449
## 3                  Midlands     0-18 0.22564656
## 4           East of England     0-18 0.22810783
## 5                    London     0-18 0.23764782
## 6                South East     0-18 0.22458811
## 7                South West     0-18 0.20799797
## 8                North West    19-69 0.64274078
## 9  North East and Yorkshire    19-69 0.64437753
## 10                 Midlands    19-69 0.63876675
## 11          East of England    19-69 0.63034229
## 12                   London    19-69 0.67820084
## 13               South East    19-69 0.63267336
## 14               South West    19-69 0.63176131
## 15               North West   70-120 0.13187323
## 16 North East and Yorkshire   70-120 0.13685797
## 17                 Midlands   70-120 0.13558669
## 18          East of England   70-120 0.14154988
## 19                   London   70-120 0.08415135
## 20               South East   70-120 0.14273853
## 21               South West   70-120 0.16024072

Finally, we import publically available deaths per NHS region:


dth <- import_deaths() %>%
  mutate(nhs_region = str_to_title(gsub("_"," ",nhs_region)))

#truncation to account for reporting delay
delay_max <- 21

dth$nhs_region <- gsub(" Of ", " of ", dth$nhs_region)
dth$nhs_region <- gsub(" And ", " and ", dth$nhs_region)
dth
##     date_report               nhs_region deaths
## 1    2020-03-01          East of England      0
## 2    2020-03-02          East of England      1
## 3    2020-03-03          East of England      0
## 4    2020-03-04          East of England      0
## 5    2020-03-05          East of England      0
## 6    2020-03-06          East of England      1
## 7    2020-03-07          East of England      0
## 8    2020-03-08          East of England      0
## 9    2020-03-09          East of England      1
## 10   2020-03-10          East of England      0
## 11   2020-03-11          East of England      0
## 12   2020-03-12          East of England      0
## 13   2020-03-13          East of England      1
## 14   2020-03-14          East of England      2
## 15   2020-03-15          East of England      2
## 16   2020-03-16          East of England      1
## 17   2020-03-17          East of England      1
## 18   2020-03-18          East of England      5
## 19   2020-03-19          East of England      4
## 20   2020-03-20          East of England      2
## 21   2020-03-21          East of England     11
## 22   2020-03-22          East of England     12
## 23   2020-03-23          East of England     11
## 24   2020-03-24          East of England     19
## 25   2020-03-25          East of England     26
## 26   2020-03-26          East of England     36
## 27   2020-03-27          East of England     38
## 28   2020-03-28          East of England     28
## 29   2020-03-29          East of England     43
## 30   2020-03-30          East of England     45
## 31   2020-03-31          East of England     70
## 32   2020-04-01          East of England     62
## 33   2020-04-02          East of England     64
## 34   2020-04-03          East of England     80
## 35   2020-04-04          East of England     71
## 36   2020-04-05          East of England     76
## 37   2020-04-06          East of England     71
## 38   2020-04-07          East of England     93
## 39   2020-04-08          East of England    111
## 40   2020-04-09          East of England     87
## 41   2020-04-10          East of England     74
## 42   2020-04-11          East of England     91
## 43   2020-04-12          East of England    101
## 44   2020-04-13          East of England     78
## 45   2020-04-14          East of England     61
## 46   2020-04-15          East of England     82
## 47   2020-04-16          East of England     74
## 48   2020-04-17          East of England     86
## 49   2020-04-18          East of England     64
## 50   2020-04-19          East of England     67
## 51   2020-04-20          East of England     67
## 52   2020-04-21          East of England     75
## 53   2020-04-22          East of England     67
## 54   2020-04-23          East of England     49
## 55   2020-04-24          East of England     66
## 56   2020-04-25          East of England     54
## 57   2020-04-26          East of England     48
## 58   2020-04-27          East of England     46
## 59   2020-04-28          East of England     58
## 60   2020-04-29          East of England     32
## 61   2020-04-30          East of England     45
## 62   2020-05-01          East of England     49
## 63   2020-05-02          East of England     29
## 64   2020-05-03          East of England     41
## 65   2020-05-04          East of England     19
## 66   2020-05-05          East of England     36
## 67   2020-05-06          East of England     31
## 68   2020-05-07          East of England     33
## 69   2020-05-08          East of England     33
## 70   2020-05-09          East of England     29
## 71   2020-05-10          East of England     22
## 72   2020-05-11          East of England     18
## 73   2020-05-12          East of England     21
## 74   2020-05-13          East of England     27
## 75   2020-05-14          East of England     26
## 76   2020-05-15          East of England     19
## 77   2020-05-16          East of England     26
## 78   2020-05-17          East of England     17
## 79   2020-05-18          East of England     25
## 80   2020-05-19          East of England     15
## 81   2020-05-20          East of England     26
## 82   2020-05-21          East of England     21
## 83   2020-05-22          East of England     13
## 84   2020-05-23          East of England     12
## 85   2020-05-24          East of England     17
## 86   2020-05-25          East of England     25
## 87   2020-05-26          East of England     14
## 88   2020-05-27          East of England     12
## 89   2020-05-28          East of England     17
## 90   2020-05-29          East of England     16
## 91   2020-05-30          East of England      9
## 92   2020-05-31          East of England      8
## 93   2020-06-01          East of England     17
## 94   2020-06-02          East of England     14
## 95   2020-06-03          East of England     10
## 96   2020-06-04          East of England      7
## 97   2020-06-05          East of England     12
## 98   2020-06-06          East of England      5
## 99   2020-06-07          East of England      9
## 100  2020-06-08          East of England      5
## 101  2020-06-09          East of England      6
## 102  2020-06-10          East of England      8
## 103  2020-06-11          East of England      0
## 104  2020-06-12          East of England      9
## 105  2020-06-13          East of England      5
## 106  2020-06-14          East of England      4
## 107  2020-06-15          East of England      6
## 108  2020-06-16          East of England      2
## 109  2020-06-17          East of England      4
## 110  2020-06-18          East of England      1
## 111  2020-03-01                   London      0
## 112  2020-03-02                   London      0
## 113  2020-03-03                   London      0
## 114  2020-03-04                   London      0
## 115  2020-03-05                   London      0
## 116  2020-03-06                   London      1
## 117  2020-03-07                   London      0
## 118  2020-03-08                   London      0
## 119  2020-03-09                   London      1
## 120  2020-03-10                   London      0
## 121  2020-03-11                   London      6
## 122  2020-03-12                   London      6
## 123  2020-03-13                   London     10
## 124  2020-03-14                   London     14
## 125  2020-03-15                   London     10
## 126  2020-03-16                   London     15
## 127  2020-03-17                   London     23
## 128  2020-03-18                   London     27
## 129  2020-03-19                   London     25
## 130  2020-03-20                   London     44
## 131  2020-03-21                   London     49
## 132  2020-03-22                   London     54
## 133  2020-03-23                   London     63
## 134  2020-03-24                   London     87
## 135  2020-03-25                   London    113
## 136  2020-03-26                   London    129
## 137  2020-03-27                   London    130
## 138  2020-03-28                   London    122
## 139  2020-03-29                   London    146
## 140  2020-03-30                   London    149
## 141  2020-03-31                   London    181
## 142  2020-04-01                   London    202
## 143  2020-04-02                   London    190
## 144  2020-04-03                   London    196
## 145  2020-04-04                   London    230
## 146  2020-04-05                   London    195
## 147  2020-04-06                   London    197
## 148  2020-04-07                   London    220
## 149  2020-04-08                   London    238
## 150  2020-04-09                   London    206
## 151  2020-04-10                   London    170
## 152  2020-04-11                   London    177
## 153  2020-04-12                   London    158
## 154  2020-04-13                   London    166
## 155  2020-04-14                   London    144
## 156  2020-04-15                   London    142
## 157  2020-04-16                   London    139
## 158  2020-04-17                   London    100
## 159  2020-04-18                   London    101
## 160  2020-04-19                   London    103
## 161  2020-04-20                   London     95
## 162  2020-04-21                   London     94
## 163  2020-04-22                   London    109
## 164  2020-04-23                   London     77
## 165  2020-04-24                   London     71
## 166  2020-04-25                   London     58
## 167  2020-04-26                   London     53
## 168  2020-04-27                   London     51
## 169  2020-04-28                   London     43
## 170  2020-04-29                   London     44
## 171  2020-04-30                   London     40
## 172  2020-05-01                   London     41
## 173  2020-05-02                   London     40
## 174  2020-05-03                   London     36
## 175  2020-05-04                   London     30
## 176  2020-05-05                   London     25
## 177  2020-05-06                   London     37
## 178  2020-05-07                   London     37
## 179  2020-05-08                   London     30
## 180  2020-05-09                   London     23
## 181  2020-05-10                   London     26
## 182  2020-05-11                   London     18
## 183  2020-05-12                   London     18
## 184  2020-05-13                   London     16
## 185  2020-05-14                   London     20
## 186  2020-05-15                   London     18
## 187  2020-05-16                   London     14
## 188  2020-05-17                   London     15
## 189  2020-05-18                   London      9
## 190  2020-05-19                   London     14
## 191  2020-05-20                   London     19
## 192  2020-05-21                   London     12
## 193  2020-05-22                   London     10
## 194  2020-05-23                   London      6
## 195  2020-05-24                   London      7
## 196  2020-05-25                   London      9
## 197  2020-05-26                   London     12
## 198  2020-05-27                   London      7
## 199  2020-05-28                   London      8
## 200  2020-05-29                   London      7
## 201  2020-05-30                   London     12
## 202  2020-05-31                   London      6
## 203  2020-06-01                   London     10
## 204  2020-06-02                   London      7
## 205  2020-06-03                   London      6
## 206  2020-06-04                   London      8
## 207  2020-06-05                   London      4
## 208  2020-06-06                   London      0
## 209  2020-06-07                   London      4
## 210  2020-06-08                   London      5
## 211  2020-06-09                   London      2
## 212  2020-06-10                   London      7
## 213  2020-06-11                   London      5
## 214  2020-06-12                   London      3
## 215  2020-06-13                   London      3
## 216  2020-06-14                   London      2
## 217  2020-06-15                   London      1
## 218  2020-06-16                   London      2
## 219  2020-06-17                   London      1
## 220  2020-06-18                   London      0
## 221  2020-03-01                 Midlands      0
## 222  2020-03-02                 Midlands      0
## 223  2020-03-03                 Midlands      1
## 224  2020-03-04                 Midlands      0
## 225  2020-03-05                 Midlands      0
## 226  2020-03-06                 Midlands      0
## 227  2020-03-07                 Midlands      0
## 228  2020-03-08                 Midlands      3
## 229  2020-03-09                 Midlands      1
## 230  2020-03-10                 Midlands      0
## 231  2020-03-11                 Midlands      2
## 232  2020-03-12                 Midlands      6
## 233  2020-03-13                 Midlands      5
## 234  2020-03-14                 Midlands      4
## 235  2020-03-15                 Midlands      5
## 236  2020-03-16                 Midlands     11
## 237  2020-03-17                 Midlands      8
## 238  2020-03-18                 Midlands     13
## 239  2020-03-19                 Midlands      8
## 240  2020-03-20                 Midlands     28
## 241  2020-03-21                 Midlands     13
## 242  2020-03-22                 Midlands     31
## 243  2020-03-23                 Midlands     33
## 244  2020-03-24                 Midlands     41
## 245  2020-03-25                 Midlands     48
## 246  2020-03-26                 Midlands     64
## 247  2020-03-27                 Midlands     72
## 248  2020-03-28                 Midlands     89
## 249  2020-03-29                 Midlands     92
## 250  2020-03-30                 Midlands     90
## 251  2020-03-31                 Midlands    123
## 252  2020-04-01                 Midlands    140
## 253  2020-04-02                 Midlands    142
## 254  2020-04-03                 Midlands    124
## 255  2020-04-04                 Midlands    151
## 256  2020-04-05                 Midlands    164
## 257  2020-04-06                 Midlands    140
## 258  2020-04-07                 Midlands    123
## 259  2020-04-08                 Midlands    186
## 260  2020-04-09                 Midlands    139
## 261  2020-04-10                 Midlands    127
## 262  2020-04-11                 Midlands    142
## 263  2020-04-12                 Midlands    139
## 264  2020-04-13                 Midlands    120
## 265  2020-04-14                 Midlands    116
## 266  2020-04-15                 Midlands    147
## 267  2020-04-16                 Midlands    102
## 268  2020-04-17                 Midlands    118
## 269  2020-04-18                 Midlands    115
## 270  2020-04-19                 Midlands     92
## 271  2020-04-20                 Midlands    107
## 272  2020-04-21                 Midlands     86
## 273  2020-04-22                 Midlands     78
## 274  2020-04-23                 Midlands    103
## 275  2020-04-24                 Midlands     79
## 276  2020-04-25                 Midlands     72
## 277  2020-04-26                 Midlands     81
## 278  2020-04-27                 Midlands     74
## 279  2020-04-28                 Midlands     68
## 280  2020-04-29                 Midlands     53
## 281  2020-04-30                 Midlands     56
## 282  2020-05-01                 Midlands     64
## 283  2020-05-02                 Midlands     51
## 284  2020-05-03                 Midlands     52
## 285  2020-05-04                 Midlands     61
## 286  2020-05-05                 Midlands     58
## 287  2020-05-06                 Midlands     59
## 288  2020-05-07                 Midlands     48
## 289  2020-05-08                 Midlands     34
## 290  2020-05-09                 Midlands     37
## 291  2020-05-10                 Midlands     42
## 292  2020-05-11                 Midlands     33
## 293  2020-05-12                 Midlands     45
## 294  2020-05-13                 Midlands     40
## 295  2020-05-14                 Midlands     37
## 296  2020-05-15                 Midlands     40
## 297  2020-05-16                 Midlands     34
## 298  2020-05-17                 Midlands     31
## 299  2020-05-18                 Midlands     34
## 300  2020-05-19                 Midlands     34
## 301  2020-05-20                 Midlands     36
## 302  2020-05-21                 Midlands     32
## 303  2020-05-22                 Midlands     27
## 304  2020-05-23                 Midlands     34
## 305  2020-05-24                 Midlands     19
## 306  2020-05-25                 Midlands     26
## 307  2020-05-26                 Midlands     33
## 308  2020-05-27                 Midlands     29
## 309  2020-05-28                 Midlands     27
## 310  2020-05-29                 Midlands     20
## 311  2020-05-30                 Midlands     20
## 312  2020-05-31                 Midlands     22
## 313  2020-06-01                 Midlands     20
## 314  2020-06-02                 Midlands     22
## 315  2020-06-03                 Midlands     24
## 316  2020-06-04                 Midlands     15
## 317  2020-06-05                 Midlands     21
## 318  2020-06-06                 Midlands     20
## 319  2020-06-07                 Midlands     16
## 320  2020-06-08                 Midlands     15
## 321  2020-06-09                 Midlands     17
## 322  2020-06-10                 Midlands     14
## 323  2020-06-11                 Midlands     13
## 324  2020-06-12                 Midlands     12
## 325  2020-06-13                 Midlands      6
## 326  2020-06-14                 Midlands     16
## 327  2020-06-15                 Midlands     11
## 328  2020-06-16                 Midlands     10
## 329  2020-06-17                 Midlands      7
## 330  2020-06-18                 Midlands      0
## 331  2020-03-01 North East and Yorkshire      0
## 332  2020-03-02 North East and Yorkshire      0
## 333  2020-03-03 North East and Yorkshire      0
## 334  2020-03-04 North East and Yorkshire      0
## 335  2020-03-05 North East and Yorkshire      0
## 336  2020-03-06 North East and Yorkshire      0
## 337  2020-03-07 North East and Yorkshire      0
## 338  2020-03-08 North East and Yorkshire      0
## 339  2020-03-09 North East and Yorkshire      0
## 340  2020-03-10 North East and Yorkshire      0
## 341  2020-03-11 North East and Yorkshire      0
## 342  2020-03-12 North East and Yorkshire      0
## 343  2020-03-13 North East and Yorkshire      0
## 344  2020-03-14 North East and Yorkshire      0
## 345  2020-03-15 North East and Yorkshire      2
## 346  2020-03-16 North East and Yorkshire      3
## 347  2020-03-17 North East and Yorkshire      1
## 348  2020-03-18 North East and Yorkshire      2
## 349  2020-03-19 North East and Yorkshire      6
## 350  2020-03-20 North East and Yorkshire      5
## 351  2020-03-21 North East and Yorkshire      6
## 352  2020-03-22 North East and Yorkshire      7
## 353  2020-03-23 North East and Yorkshire      9
## 354  2020-03-24 North East and Yorkshire      8
## 355  2020-03-25 North East and Yorkshire     18
## 356  2020-03-26 North East and Yorkshire     21
## 357  2020-03-27 North East and Yorkshire     28
## 358  2020-03-28 North East and Yorkshire     35
## 359  2020-03-29 North East and Yorkshire     38
## 360  2020-03-30 North East and Yorkshire     64
## 361  2020-03-31 North East and Yorkshire     60
## 362  2020-04-01 North East and Yorkshire     67
## 363  2020-04-02 North East and Yorkshire     74
## 364  2020-04-03 North East and Yorkshire    100
## 365  2020-04-04 North East and Yorkshire    105
## 366  2020-04-05 North East and Yorkshire     92
## 367  2020-04-06 North East and Yorkshire     96
## 368  2020-04-07 North East and Yorkshire    102
## 369  2020-04-08 North East and Yorkshire    107
## 370  2020-04-09 North East and Yorkshire    111
## 371  2020-04-10 North East and Yorkshire    117
## 372  2020-04-11 North East and Yorkshire     98
## 373  2020-04-12 North East and Yorkshire     84
## 374  2020-04-13 North East and Yorkshire     94
## 375  2020-04-14 North East and Yorkshire    107
## 376  2020-04-15 North East and Yorkshire     96
## 377  2020-04-16 North East and Yorkshire    103
## 378  2020-04-17 North East and Yorkshire     88
## 379  2020-04-18 North East and Yorkshire     95
## 380  2020-04-19 North East and Yorkshire     88
## 381  2020-04-20 North East and Yorkshire    100
## 382  2020-04-21 North East and Yorkshire     76
## 383  2020-04-22 North East and Yorkshire     84
## 384  2020-04-23 North East and Yorkshire     63
## 385  2020-04-24 North East and Yorkshire     72
## 386  2020-04-25 North East and Yorkshire     69
## 387  2020-04-26 North East and Yorkshire     65
## 388  2020-04-27 North East and Yorkshire     65
## 389  2020-04-28 North East and Yorkshire     57
## 390  2020-04-29 North East and Yorkshire     69
## 391  2020-04-30 North East and Yorkshire     57
## 392  2020-05-01 North East and Yorkshire     64
## 393  2020-05-02 North East and Yorkshire     48
## 394  2020-05-03 North East and Yorkshire     40
## 395  2020-05-04 North East and Yorkshire     49
## 396  2020-05-05 North East and Yorkshire     40
## 397  2020-05-06 North East and Yorkshire     51
## 398  2020-05-07 North East and Yorkshire     45
## 399  2020-05-08 North East and Yorkshire     42
## 400  2020-05-09 North East and Yorkshire     44
## 401  2020-05-10 North East and Yorkshire     40
## 402  2020-05-11 North East and Yorkshire     29
## 403  2020-05-12 North East and Yorkshire     27
## 404  2020-05-13 North East and Yorkshire     28
## 405  2020-05-14 North East and Yorkshire     30
## 406  2020-05-15 North East and Yorkshire     32
## 407  2020-05-16 North East and Yorkshire     35
## 408  2020-05-17 North East and Yorkshire     26
## 409  2020-05-18 North East and Yorkshire     29
## 410  2020-05-19 North East and Yorkshire     27
## 411  2020-05-20 North East and Yorkshire     21
## 412  2020-05-21 North East and Yorkshire     33
## 413  2020-05-22 North East and Yorkshire     22
## 414  2020-05-23 North East and Yorkshire     18
## 415  2020-05-24 North East and Yorkshire     25
## 416  2020-05-25 North East and Yorkshire     21
## 417  2020-05-26 North East and Yorkshire     21
## 418  2020-05-27 North East and Yorkshire     22
## 419  2020-05-28 North East and Yorkshire     20
## 420  2020-05-29 North East and Yorkshire     25
## 421  2020-05-30 North East and Yorkshire     20
## 422  2020-05-31 North East and Yorkshire     20
## 423  2020-06-01 North East and Yorkshire     16
## 424  2020-06-02 North East and Yorkshire     22
## 425  2020-06-03 North East and Yorkshire     22
## 426  2020-06-04 North East and Yorkshire     17
## 427  2020-06-05 North East and Yorkshire     17
## 428  2020-06-06 North East and Yorkshire     21
## 429  2020-06-07 North East and Yorkshire     13
## 430  2020-06-08 North East and Yorkshire     11
## 431  2020-06-09 North East and Yorkshire     11
## 432  2020-06-10 North East and Yorkshire     17
## 433  2020-06-11 North East and Yorkshire      7
## 434  2020-06-12 North East and Yorkshire      9
## 435  2020-06-13 North East and Yorkshire     10
## 436  2020-06-14 North East and Yorkshire     11
## 437  2020-06-15 North East and Yorkshire      8
## 438  2020-06-16 North East and Yorkshire     10
## 439  2020-06-17 North East and Yorkshire      5
## 440  2020-06-18 North East and Yorkshire      1
## 441  2020-03-01               North West      0
## 442  2020-03-02               North West      0
## 443  2020-03-03               North West      0
## 444  2020-03-04               North West      0
## 445  2020-03-05               North West      1
## 446  2020-03-06               North West      0
## 447  2020-03-07               North West      0
## 448  2020-03-08               North West      1
## 449  2020-03-09               North West      0
## 450  2020-03-10               North West      0
## 451  2020-03-11               North West      0
## 452  2020-03-12               North West      2
## 453  2020-03-13               North West      3
## 454  2020-03-14               North West      1
## 455  2020-03-15               North West      4
## 456  2020-03-16               North West      2
## 457  2020-03-17               North West      4
## 458  2020-03-18               North West      6
## 459  2020-03-19               North West      7
## 460  2020-03-20               North West     10
## 461  2020-03-21               North West     11
## 462  2020-03-22               North West     13
## 463  2020-03-23               North West     15
## 464  2020-03-24               North West     21
## 465  2020-03-25               North West     21
## 466  2020-03-26               North West     29
## 467  2020-03-27               North West     35
## 468  2020-03-28               North West     28
## 469  2020-03-29               North West     46
## 470  2020-03-30               North West     67
## 471  2020-03-31               North West     52
## 472  2020-04-01               North West     86
## 473  2020-04-02               North West     96
## 474  2020-04-03               North West     95
## 475  2020-04-04               North West     98
## 476  2020-04-05               North West    102
## 477  2020-04-06               North West    100
## 478  2020-04-07               North West    135
## 479  2020-04-08               North West    127
## 480  2020-04-09               North West    119
## 481  2020-04-10               North West    117
## 482  2020-04-11               North West    138
## 483  2020-04-12               North West    125
## 484  2020-04-13               North West    129
## 485  2020-04-14               North West    131
## 486  2020-04-15               North West    114
## 487  2020-04-16               North West    135
## 488  2020-04-17               North West     98
## 489  2020-04-18               North West    113
## 490  2020-04-19               North West     71
## 491  2020-04-20               North West     83
## 492  2020-04-21               North West     76
## 493  2020-04-22               North West     86
## 494  2020-04-23               North West     85
## 495  2020-04-24               North West     66
## 496  2020-04-25               North West     65
## 497  2020-04-26               North West     55
## 498  2020-04-27               North West     54
## 499  2020-04-28               North West     57
## 500  2020-04-29               North West     62
## 501  2020-04-30               North West     59
## 502  2020-05-01               North West     45
## 503  2020-05-02               North West     56
## 504  2020-05-03               North West     55
## 505  2020-05-04               North West     48
## 506  2020-05-05               North West     48
## 507  2020-05-06               North West     44
## 508  2020-05-07               North West     49
## 509  2020-05-08               North West     42
## 510  2020-05-09               North West     30
## 511  2020-05-10               North West     41
## 512  2020-05-11               North West     34
## 513  2020-05-12               North West     38
## 514  2020-05-13               North West     25
## 515  2020-05-14               North West     26
## 516  2020-05-15               North West     33
## 517  2020-05-16               North West     32
## 518  2020-05-17               North West     24
## 519  2020-05-18               North West     31
## 520  2020-05-19               North West     35
## 521  2020-05-20               North West     27
## 522  2020-05-21               North West     26
## 523  2020-05-22               North West     26
## 524  2020-05-23               North West     31
## 525  2020-05-24               North West     26
## 526  2020-05-25               North West     31
## 527  2020-05-26               North West     27
## 528  2020-05-27               North West     27
## 529  2020-05-28               North West     28
## 530  2020-05-29               North West     20
## 531  2020-05-30               North West     17
## 532  2020-05-31               North West     13
## 533  2020-06-01               North West     12
## 534  2020-06-02               North West     27
## 535  2020-06-03               North West     21
## 536  2020-06-04               North West     22
## 537  2020-06-05               North West     15
## 538  2020-06-06               North West     23
## 539  2020-06-07               North West     19
## 540  2020-06-08               North West     20
## 541  2020-06-09               North West     15
## 542  2020-06-10               North West     14
## 543  2020-06-11               North West     16
## 544  2020-06-12               North West      7
## 545  2020-06-13               North West      8
## 546  2020-06-14               North West     15
## 547  2020-06-15               North West     14
## 548  2020-06-16               North West      8
## 549  2020-06-17               North West      9
## 550  2020-06-18               North West      0
## 551  2020-03-01               South East      0
## 552  2020-03-02               South East      0
## 553  2020-03-03               South East      1
## 554  2020-03-04               South East      0
## 555  2020-03-05               South East      1
## 556  2020-03-06               South East      0
## 557  2020-03-07               South East      0
## 558  2020-03-08               South East      1
## 559  2020-03-09               South East      1
## 560  2020-03-10               South East      1
## 561  2020-03-11               South East      1
## 562  2020-03-12               South East      0
## 563  2020-03-13               South East      1
## 564  2020-03-14               South East      1
## 565  2020-03-15               South East      5
## 566  2020-03-16               South East      8
## 567  2020-03-17               South East      7
## 568  2020-03-18               South East     10
## 569  2020-03-19               South East      9
## 570  2020-03-20               South East     13
## 571  2020-03-21               South East      7
## 572  2020-03-22               South East     25
## 573  2020-03-23               South East     20
## 574  2020-03-24               South East     22
## 575  2020-03-25               South East     29
## 576  2020-03-26               South East     35
## 577  2020-03-27               South East     34
## 578  2020-03-28               South East     36
## 579  2020-03-29               South East     55
## 580  2020-03-30               South East     58
## 581  2020-03-31               South East     65
## 582  2020-04-01               South East     66
## 583  2020-04-02               South East     55
## 584  2020-04-03               South East     72
## 585  2020-04-04               South East     80
## 586  2020-04-05               South East     82
## 587  2020-04-06               South East     88
## 588  2020-04-07               South East    100
## 589  2020-04-08               South East     83
## 590  2020-04-09               South East    104
## 591  2020-04-10               South East     88
## 592  2020-04-11               South East     88
## 593  2020-04-12               South East     88
## 594  2020-04-13               South East     84
## 595  2020-04-14               South East     65
## 596  2020-04-15               South East     72
## 597  2020-04-16               South East     56
## 598  2020-04-17               South East     86
## 599  2020-04-18               South East     57
## 600  2020-04-19               South East     70
## 601  2020-04-20               South East     87
## 602  2020-04-21               South East     50
## 603  2020-04-22               South East     54
## 604  2020-04-23               South East     57
## 605  2020-04-24               South East     64
## 606  2020-04-25               South East     51
## 607  2020-04-26               South East     51
## 608  2020-04-27               South East     40
## 609  2020-04-28               South East     40
## 610  2020-04-29               South East     47
## 611  2020-04-30               South East     29
## 612  2020-05-01               South East     37
## 613  2020-05-02               South East     36
## 614  2020-05-03               South East     17
## 615  2020-05-04               South East     35
## 616  2020-05-05               South East     29
## 617  2020-05-06               South East     25
## 618  2020-05-07               South East     27
## 619  2020-05-08               South East     26
## 620  2020-05-09               South East     28
## 621  2020-05-10               South East     19
## 622  2020-05-11               South East     25
## 623  2020-05-12               South East     27
## 624  2020-05-13               South East     18
## 625  2020-05-14               South East     32
## 626  2020-05-15               South East     24
## 627  2020-05-16               South East     22
## 628  2020-05-17               South East     18
## 629  2020-05-18               South East     22
## 630  2020-05-19               South East     12
## 631  2020-05-20               South East     22
## 632  2020-05-21               South East     14
## 633  2020-05-22               South East     17
## 634  2020-05-23               South East     21
## 635  2020-05-24               South East     17
## 636  2020-05-25               South East     13
## 637  2020-05-26               South East     19
## 638  2020-05-27               South East     18
## 639  2020-05-28               South East     12
## 640  2020-05-29               South East     21
## 641  2020-05-30               South East      8
## 642  2020-05-31               South East     10
## 643  2020-06-01               South East     11
## 644  2020-06-02               South East     13
## 645  2020-06-03               South East     17
## 646  2020-06-04               South East     11
## 647  2020-06-05               South East     11
## 648  2020-06-06               South East     10
## 649  2020-06-07               South East     11
## 650  2020-06-08               South East      7
## 651  2020-06-09               South East      9
## 652  2020-06-10               South East     10
## 653  2020-06-11               South East      5
## 654  2020-06-12               South East      5
## 655  2020-06-13               South East      4
## 656  2020-06-14               South East      6
## 657  2020-06-15               South East      7
## 658  2020-06-16               South East      9
## 659  2020-06-17               South East      6
## 660  2020-06-18               South East      0
## 661  2020-03-01               South West      0
## 662  2020-03-02               South West      0
## 663  2020-03-03               South West      0
## 664  2020-03-04               South West      0
## 665  2020-03-05               South West      0
## 666  2020-03-06               South West      0
## 667  2020-03-07               South West      0
## 668  2020-03-08               South West      0
## 669  2020-03-09               South West      0
## 670  2020-03-10               South West      0
## 671  2020-03-11               South West      1
## 672  2020-03-12               South West      0
## 673  2020-03-13               South West      0
## 674  2020-03-14               South West      1
## 675  2020-03-15               South West      0
## 676  2020-03-16               South West      0
## 677  2020-03-17               South West      2
## 678  2020-03-18               South West      2
## 679  2020-03-19               South West      4
## 680  2020-03-20               South West      3
## 681  2020-03-21               South West      6
## 682  2020-03-22               South West      7
## 683  2020-03-23               South West      8
## 684  2020-03-24               South West      7
## 685  2020-03-25               South West      9
## 686  2020-03-26               South West     11
## 687  2020-03-27               South West     13
## 688  2020-03-28               South West     21
## 689  2020-03-29               South West     18
## 690  2020-03-30               South West     23
## 691  2020-03-31               South West     23
## 692  2020-04-01               South West     22
## 693  2020-04-02               South West     23
## 694  2020-04-03               South West     30
## 695  2020-04-04               South West     42
## 696  2020-04-05               South West     32
## 697  2020-04-06               South West     34
## 698  2020-04-07               South West     39
## 699  2020-04-08               South West     47
## 700  2020-04-09               South West     24
## 701  2020-04-10               South West     46
## 702  2020-04-11               South West     43
## 703  2020-04-12               South West     23
## 704  2020-04-13               South West     27
## 705  2020-04-14               South West     24
## 706  2020-04-15               South West     32
## 707  2020-04-16               South West     29
## 708  2020-04-17               South West     33
## 709  2020-04-18               South West     25
## 710  2020-04-19               South West     31
## 711  2020-04-20               South West     26
## 712  2020-04-21               South West     26
## 713  2020-04-22               South West     23
## 714  2020-04-23               South West     17
## 715  2020-04-24               South West     19
## 716  2020-04-25               South West     15
## 717  2020-04-26               South West     27
## 718  2020-04-27               South West     13
## 719  2020-04-28               South West     17
## 720  2020-04-29               South West     15
## 721  2020-04-30               South West     26
## 722  2020-05-01               South West      6
## 723  2020-05-02               South West      7
## 724  2020-05-03               South West     10
## 725  2020-05-04               South West     17
## 726  2020-05-05               South West     14
## 727  2020-05-06               South West     19
## 728  2020-05-07               South West     16
## 729  2020-05-08               South West      6
## 730  2020-05-09               South West     11
## 731  2020-05-10               South West      5
## 732  2020-05-11               South West      8
## 733  2020-05-12               South West      7
## 734  2020-05-13               South West      7
## 735  2020-05-14               South West      6
## 736  2020-05-15               South West      4
## 737  2020-05-16               South West      4
## 738  2020-05-17               South West      6
## 739  2020-05-18               South West      4
## 740  2020-05-19               South West      6
## 741  2020-05-20               South West      1
## 742  2020-05-21               South West      9
## 743  2020-05-22               South West      6
## 744  2020-05-23               South West      6
## 745  2020-05-24               South West      3
## 746  2020-05-25               South West      8
## 747  2020-05-26               South West     11
## 748  2020-05-27               South West      5
## 749  2020-05-28               South West     10
## 750  2020-05-29               South West      7
## 751  2020-05-30               South West      3
## 752  2020-05-31               South West      2
## 753  2020-06-01               South West      7
## 754  2020-06-02               South West      2
## 755  2020-06-03               South West      5
## 756  2020-06-04               South West      2
## 757  2020-06-05               South West      2
## 758  2020-06-06               South West      1
## 759  2020-06-07               South West      3
## 760  2020-06-08               South West      3
## 761  2020-06-09               South West      0
## 762  2020-06-10               South West      0
## 763  2020-06-11               South West      2
## 764  2020-06-12               South West      2
## 765  2020-06-13               South West      2
## 766  2020-06-14               South West      0
## 767  2020-06-15               South West      1
## 768  2020-06-16               South West      1
## 769  2020-06-17               South West      0
## 770  2020-06-18               South West      0

1.5 Completion date

We extract the completion date from the NHS Pathways file timestamp:


database_date <- attr(x, "timestamp")
database_date
## [1] "2020-06-18"

The completion date of the NHS Pathways data is Thursday 18 Jun 2020.

1.6 Auxiliary functions

These are functions which will be used further in the analyses.

Function to estimate the generalised R-squared as the proportion of deviance explained by a given model:


## Function to calculate R2 for Poisson model
## not adjusted for model complexity but all models have the same DF here

Rsq <- function(x) {
  1 - (x$deviance / x$null.deviance)
}

Function to extract growth rates per region as well as halving times, and the associated 95% confidence intervals:


## function to extract the coefficients, find the level of the intercept,
## reconstruct the values of r, get confidence intervals

get_r <- function(model) {
  ##  extract coefficients and conf int
  out <- data.frame(r = coef(model))  %>%
    rownames_to_column("var") %>% 
    cbind(confint(model)) %>%
    filter(!grepl("day_of_week", var)) %>% 
    filter(grepl("day", var)) %>%
    rename(lower_95 = "2.5 %",
           upper_95 = "97.5 %") %>%
    mutate(var = sub("day:", "", var))
  
  ## reconstruct values: intercept + region-coefficient
  for (i in 2:nrow(out)) {
    out[i, -1] <- out[1, -1] + out[i, -1]
  }
  
  ## find the name of the intercept, restore regions names
  out <- out %>%
    mutate(nhs_region = model$xlevels$nhs_region) %>%
    select(nhs_region, everything(), -var)
  
  ## find halving times
  halving <- log(0.5) / out[,-1] %>%
    rename(halving_t = r,
           halving_t_lower_95 = lower_95,
           halving_t_upper_95 = upper_95)
  
  ## set halving times with exclusion intervals to NA
  no_halving <- out$lower_95 < 0 & out$upper_95 > 0
  halving[no_halving, ] <- NA_real_
  
  ## return all data
  cbind(out, halving)
  
}

Functions used in the correlation analysis between NHS Pathways reports and deaths:

## Function to calculate Pearson's correlation between deaths and lagged
## reports. Note that `pearson` can be replaced with `spearman` for rank
## correlation.

getcor <- function(x, ndx) {
  return(cor(x$deaths[ndx],
             x$note_lag[ndx],
             use = "complete.obs",
             method = "pearson"))
}

## Catch if sample size throws an error
getcor2 <- possibly(getcor, otherwise = NA)

getboot <- function(x) {
  result <- boot::boot.ci(boot::boot(x, getcor2, R = 1000), 
                           type = "bca")
  return(data.frame(n = sum(!is.na(x$note_lag) & !is.na(x$deaths)),
                    r = result$t0,
                    r_low = result$bca[4],
                    r_hi = result$bca[5]))
}

Function to classify the day of the week into weekend, Monday, and the rest:


## Fn to add day of week
day_of_week <- function(df) {
  df %>% 
    dplyr::mutate(day_of_week = lubridate::wday(date, label = TRUE)) %>% 
    dplyr::mutate(day_of_week = dplyr::case_when(
      day_of_week %in% c("Sat", "Sun") ~ "weekend",
      day_of_week %in% c("Mon") ~ "monday",
      !(day_of_week %in% c("Sat", "Sun", "Mon")) ~ "rest_of_week"
    ) %>% 
      factor(levels = c("rest_of_week", "monday", "weekend")))
}

Custom color palettes, color scales, and vectors of colors:


pal <- c("#006212",
         "#ae3cab",
         "#00db90",
         "#960c00",
         "#55aaff",
         "#ff7e78",
         "#00388d")

age.pal <- viridis::viridis(3,begin = 0.1, end = 0.7)

3 Comparison with deaths time series

3.1 Outline

We want to explore the correlation between NHS Pathways reports and deaths, and assess the potential for reports to be used as an early warning system for disease resurgence.

Death data are publically available. We truncate the time series to avoid bias from reporting delay - we assume a conservative delay of three weeks.

3.2 Lagged correlation

We calculate Pearson’s correlation coefficient between deaths and NHS Pathways notifications using different lags. Confidence intervals are obtained using bootstrap. Note that results were also confirmed using Spearman’s rank correlation.

First we join the NHS Pathways and death data, and aggregate over all England:

## truncate death data for reporting delay
trunc_date <- max(dth$date_report) - delay_max

dth_trunc <- dth %>%
  rename(date = date_report) %>%
  filter(date <= trunc_date) 

## join with notification data
all_data <- x %>% 
  filter(!is.na(nhs_region)) %>%
  group_by(date, nhs_region) %>%
  summarise(count = sum(count, na.rm = T)) %>%
  ungroup %>%
  inner_join(dth_trunc,
             by = c("date","nhs_region"))

all_tot <- all_data %>%
  group_by(date) %>%
  summarise(count = sum(count, na.rm = TRUE),
            deaths = sum(deaths, na.rm = TRUE)) 

We calculate correlation with lagged NHS Pathways reports from 0 to 30 days behind deaths:


## Calculate all correlations + bootstrap CIs
lag_cor <- data.frame()
for (i in 0:30) {
  
  ## lag reports
  summary <- all_tot %>% 
    mutate(note_lag = lag(count, i)) %>%
    ## calculate rank correlation and bootstrap CI
    getboot(.) %>%
    mutate(lag = i)

  lag_cor <- bind_rows(lag_cor, summary)
}

cor_vs_lag <- ggplot(lag_cor, aes(lag, r)) +
  theme_bw() +
  geom_ribbon(aes(ymin = r_low, ymax = r_hi), alpha = 0.2) +
  geom_hline(yintercept = 0, lty = "longdash") +
  geom_point() +
  geom_line() +
  labs(x = "Lag between NHS pathways and death data (days)",
       y = "Pearson's correlation") +
  large_txt
cor_vs_lag


l_opt <- which.max(lag_cor$r)

This analysis suggests that the best lag is 23 days. We then compare and plot the number of deaths reported against the number of NHS Pathways reports lagged by 23 days.


all_tot <- all_tot %>%
  rename(date_death = date) %>%
  mutate(note_lag = lag(count, lag_cor$lag[l_opt]),
         note_lag_c = (note_lag - mean(note_lag, na.rm = T)),
         date_note = lag(date_death,16))

lag_mod <- glm(deaths ~ note_lag, data = all_tot, family = "quasipoisson")

summary(lag_mod)
## 
## Call:
## glm(formula = deaths ~ note_lag, family = "quasipoisson", data = all_tot)
## 
## Deviance Residuals: 
##     Min       1Q   Median       3Q      Max  
## -9.3364  -2.7683  -0.1921   2.9300   4.9242  
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 4.953e+00  5.234e-02   94.63   <2e-16 ***
## note_lag    1.157e-05  5.228e-07   22.13   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## (Dispersion parameter for quasipoisson family taken to be 10.81681)
## 
##     Null deviance: 5665.18  on 48  degrees of freedom
## Residual deviance:  522.65  on 47  degrees of freedom
##   (23 observations deleted due to missingness)
## AIC: NA
## 
## Number of Fisher Scoring iterations: 4

exp(coefficients(lag_mod))
## (Intercept)    note_lag 
##  141.615294    1.000012
exp(confint(lag_mod))
##                  2.5 %     97.5 %
## (Intercept) 127.664875 156.743494
## note_lag      1.000011   1.000013

Rsq(lag_mod)
## [1] 0.9077432

mod_fit <- as.data.frame(predict(lag_mod, type = "link", se.fit = TRUE)[1:2])

all_tot_pred <- 
  all_tot %>%
  filter(!is.na(note_lag)) %>%
  mutate(pred = mod_fit$fit,
         pred.se = mod_fit$se.fit,
         low = exp(pred - 1.96*pred.se),
         hi = exp(pred + 1.96*pred.se))


glm_fit <- all_tot_pred %>% 
    filter(!is.na(note_lag)) %>%
  ggplot(aes(x = note_lag, y = deaths)) +
  geom_point() + 
  geom_line(aes(y = exp(pred))) + 
  geom_ribbon(aes(ymin = low, ymax = hi), alpha = 0.3, col = "grey") +
  theme_bw() +
  labs(y = "Daily number of\ndeaths reported",
       x = "Daily number of NHS Pathways reports") +
  large_txt

glm_fit

4 Supplementary figures

4.1 Serial interval distribution

This is a comparison of gamma versus lognormal distribution for the serial interval used to convert r to R in our analysis. Both distributions are parameterised with mean 4.7 and standard deviation 2.9.

SI_param <- epitrix::gamma_mucv2shapescale(4.7, 2.9/4.7)
SI_distribution <- distcrete::distcrete("gamma", interval = 1,
                                        shape = SI_param$shape,
                                        scale = SI_param$scale, w = 0.5)

SI_distribution2 <- distcrete::distcrete("lnorm", interval = 1,
                                        meanlog = log(4.7),
                                        sdlog = log(2.9), w = 0.5)

SI_dist1 <- data.frame(x = SI_distribution$r(1e5)) 
SI_dist1 <- count(SI_dist1, x) %>%
    ggplot() +
    geom_col(aes(x = x, y = n)) +
    labs(x = "Serial interval (days)", y = "Frequency") +
    scale_x_continuous(breaks = seq(0, 30, 5)) +
    theme_bw()

SI_dist2 <- data.frame(x = SI_distribution2$r(1e5)) 
SI_dist2 <- count(SI_dist2, x) %>%
    ggplot() +
    geom_col(aes(x = x, y = n)) +
    labs(x = "Serial interval (days)", y = "Frequency") +
    scale_x_continuous(breaks = seq(0, 200, 20), limits = c(0, 200)) +
    theme_bw()


ggpubr::ggarrange(SI_dist1,
                  SI_dist2,
                  nrow = 1,
                  labels = "AUTO") 

4.2 Sensitivity analysis - 7 or 21 days moving window

We reproduce the window analysis with either a 7 or 21 days window for sensitivity purposes.

First with the 7 days window:

## set moving time window (1/2/3 weeks)
w <- 7

# create empty df
r_all_sliding_7days <- NULL

## make data for model
x_model_all_moving <- x %>%
  filter(!is.na(nhs_region)) %>% 
  group_by(date, nhs_region) %>%
  summarise(n = sum(count)) 

unique_dates <- unique(x_model_all_moving$date)

for (i in 1:(length(unique_dates) - w)) {
  
  date_i <- unique_dates[i]
  
  date_i_max <- date_i + w
  
  model_data <- x_model_all_moving %>%
    filter(date >= date_i & date < date_i_max) %>%
    mutate(day = as.integer(date - date_i)) %>% 
    day_of_week()
  
  
  mod <- glm(n ~ day * nhs_region + day_of_week,
             data = model_data,
             family = 'quasipoisson')
  
  # get growth rate
  r <- get_r(mod)
  r$w_min <- date_i
  r$w_max <- date_i_max
  
  # combine all estimates
  r_all_sliding_7days <- bind_rows(r_all_sliding_7days, r)
  
}

#serial interval distribution
SI_param = epitrix::gamma_mucv2shapescale(4.7, 2.9/4.7)
SI_distribution <- distcrete::distcrete("gamma", interval = 1,
                                        shape = SI_param$shape,
                                        scale = SI_param$scale,
                                        w = 0.5)

#convert growth rates r to R0
r_all_sliding_7days <- r_all_sliding_7days %>%
  mutate(R = epitrix::r2R0(r, SI_distribution),
         R_lower_95 = epitrix::r2R0(lower_95, SI_distribution),
         R_upper_95 = epitrix::r2R0(upper_95, SI_distribution))
# plot
plot_growth <-
  r_all_sliding_7days %>%
  ggplot(aes(x = w_max, y = r)) +
  geom_ribbon(aes(ymin = lower_95, ymax = upper_95, fill = nhs_region), alpha = 0.1) +
  geom_line(aes(colour = nhs_region)) +
  geom_point(aes(colour = nhs_region)) +
  geom_hline(yintercept = 0, linetype = "dashed") +
  theme_bw() +
  scale_weeks +
  theme(legend.position = "bottom",
        plot.margin = margin(0.5,1,0.5,0.5, "cm")) +
  guides(colour = guide_legend(title = "",override.aes = list(fill = NA)), fill = FALSE) +
  labs(x = "",
       y = "Estimated daily growth rate (r)") +
  scale_colour_manual(values = pal)
plot_R <- r_all_sliding_7days %>%
  ggplot(aes(x = w_max, y = R)) +
  geom_ribbon(aes(ymin = R_lower_95, ymax = R_upper_95, fill = nhs_region), alpha = 0.1) +
  geom_line(aes(colour = nhs_region)) +
  geom_point(aes(colour = nhs_region)) +
  geom_hline(yintercept = 1, linetype = "dashed") +
  theme_bw() +
  scale_weeks +
  theme(legend.position = "bottom",
        plot.margin = margin(0.5,1,0.5,0.5, "cm")) +
  guides(color = guide_legend(title = "", override.aes = list(fill = NA)), fill = FALSE) +
  labs(x = "",
       y = "Estimated effective reproduction\nnumber (Re)") +
  scale_colour_manual(values = pal)

R <- r_all_sliding_7days %>%
  mutate(lower_95 = R_lower_95, 
         upper_95 = R_upper_95,
         value = R,
         measure = "R",
         reference = 1)

r_R <- r_all_sliding_7days %>%
  mutate(measure = "r",
         value = r,
         reference = 0) %>%
  bind_rows(R)

r_R_7 <- r_R %>%
  ggplot(aes(x = w_max, y = value)) +
  geom_ribbon(aes(ymin = lower_95, ymax = upper_95, fill = nhs_region), alpha = 0.1) +
  geom_line(aes(colour = nhs_region)) +
  geom_point(aes(colour = nhs_region)) +
  geom_hline(aes(yintercept = reference), linetype = "dashed") +
  theme_bw() +
  scale_weeks +
  theme(legend.position = "bottom",
        plot.margin = margin(0.5,1,0,0, "cm"),
        strip.background = element_blank(),
        strip.placement = "outside"
  ) +
  guides(color = guide_legend(title = "", override.aes = list(fill = NA)), fill = FALSE) +
  labs(x = "", y = "") +
  scale_colour_manual(values = pal) +
  facet_grid(rows = vars(measure),
             scales = "free_y",
             switch = "y",
             labeller = as_labeller(c(r = "Daily growth rate (r)",
                                      R = "Effective reproduction\nnumber (Re)")))

Then with the 21 days window:

## set moving time window (1/2/3 weeks)
w <- 21

# create empty df
r_all_sliding_21days <- NULL

## make data for model
x_model_all_moving <- x %>%
  filter(!is.na(nhs_region)) %>% 
  group_by(date, nhs_region) %>%
  summarise(n = sum(count)) 

unique_dates <- unique(x_model_all_moving$date)

for (i in 1:(length(unique_dates) - w)) {
  
  date_i <- unique_dates[i]
  
  date_i_max <- date_i + w
  
  model_data <- x_model_all_moving %>%
    filter(date >= date_i & date < date_i_max) %>%
    mutate(day = as.integer(date - date_i)) %>% 
    day_of_week()
  
  
  mod <- glm(n ~ day * nhs_region + day_of_week,
             data = model_data,
             family = 'quasipoisson')
  
  # get growth rate
  r <- get_r(mod)
  r$w_min <- date_i
  r$w_max <- date_i_max
  
  # combine all estimates
  r_all_sliding_21days <- bind_rows(r_all_sliding_21days, r)
  
}

#serial interval distribution
SI_param = epitrix::gamma_mucv2shapescale(4.7, 2.9/4.7)
SI_distribution <- distcrete::distcrete("gamma", interval = 1,
                                        shape = SI_param$shape,
                                        scale = SI_param$scale,
                                        w = 0.5)

#convert growth rates r to R0
r_all_sliding_21days <- r_all_sliding_21days %>%
  mutate(R = epitrix::r2R0(r, SI_distribution),
         R_lower_95 = epitrix::r2R0(lower_95, SI_distribution),
         R_upper_95 = epitrix::r2R0(upper_95, SI_distribution))
# plot
plot_growth <-
  r_all_sliding_21days %>%
  ggplot(aes(x = w_max, y = r)) +
  geom_ribbon(aes(ymin = lower_95, ymax = upper_95, fill = nhs_region), alpha = 0.1) +
  geom_line(aes(colour = nhs_region)) +
  geom_point(aes(colour = nhs_region)) +
  geom_hline(yintercept = 0, linetype = "dashed") +
  theme_bw() +
  scale_weeks +
  theme(legend.position = "bottom",
        plot.margin = margin(0.5,1,0.5,0.5, "cm")) +
  guides(colour = guide_legend(title = "",override.aes = list(fill = NA)), fill = FALSE) +
  labs(x = "",
       y = "Estimated daily growth rate (r)") +
  scale_colour_manual(values = pal)
# plot
plot_R <-
  r_all_sliding_21days %>%
  ggplot(aes(x = w_max, y = R)) +
  geom_ribbon(aes(ymin = R_lower_95, ymax = R_upper_95, fill = nhs_region), alpha = 0.1) +
  geom_line(aes(colour = nhs_region)) +
  geom_point(aes(colour = nhs_region)) +
  geom_hline(yintercept = 1, linetype = "dashed") +
  theme_bw() +
  scale_weeks +
  theme(legend.position = "bottom",
        plot.margin = margin(0.5,1,0.5,0.5, "cm")) +
  guides(color = guide_legend(title = "", override.aes = list(fill = NA)), fill = FALSE) +
  labs(x = "",
       y = "Estimated effective reproduction\nnumber (Re)") +
  scale_colour_manual(values = pal)

R <- r_all_sliding_21days %>%
  mutate(lower_95 = R_lower_95, 
         upper_95 = R_upper_95,
         value = R,
         measure = "R",
         reference = 1)

r_R <- r_all_sliding_21days %>%
  mutate(measure = "r",
         value = r,
         reference = 0) %>%
  bind_rows(R)

r_R_21 <- r_R %>%
  ggplot(aes(x = w_max, y = value)) +
  geom_ribbon(aes(ymin = lower_95, ymax = upper_95, fill = nhs_region), alpha = 0.1) +
  geom_line(aes(colour = nhs_region)) +
  geom_point(aes(colour = nhs_region)) +
  geom_hline(aes(yintercept = reference), linetype = "dashed") +
  theme_bw() +
  scale_weeks +
  theme(legend.position = "bottom",
        plot.margin = margin(0.5,1,0,0, "cm"),
        strip.background = element_blank(),
        strip.placement = "outside"
  ) +
  guides(color = guide_legend(title = "", override.aes = list(fill = NA)), fill = FALSE) +
  labs(x = "", y = "") +
  scale_colour_manual(values = pal) +
  facet_grid(rows = vars(measure),
             scales = "free_y",
             switch = "y",
             labeller = as_labeller(c(r = "Daily growth rate (r)",
                                      R = "Effective reproduction\nnumber (Re)")))

And we combine both outputs into a single plot:


ggpubr::ggarrange(r_R_7,
                  r_R_21,
                  nrow = 2,
                  labels = "AUTO",
                  common.legend = TRUE,
                  legend = "bottom") 

4.3 Correlation between NHS Pathways reports and deaths by NHS region


lag_cor_reg <- data.frame()

for (i in 0:30) {

  summary <-
    all_data %>%
    group_by(nhs_region) %>%
    mutate(note_lag = lag(count, i)) %>%
    ## calculate rank correlation and bootstrap CI for each region
    group_modify(~getboot(.x)) %>%
    mutate(lag = i)
  
  lag_cor_reg <- bind_rows(lag_cor_reg, summary)
}

cor_vs_lag_reg <- 
lag_cor_reg %>%
ggplot(aes(lag, r, col = nhs_region)) +
  geom_hline(yintercept = 0, lty = "longdash") +
  geom_ribbon(aes(ymin = r_low, ymax = r_hi, col = NULL, fill = nhs_region), alpha = 0.2) +
  geom_point() +
  geom_line() +
  facet_wrap(~nhs_region) +
  scale_color_manual(values = pal) +
  scale_fill_manual(values = pal, guide = F) +  
  theme_bw() +
  labs(x = "Lag between NHS pathways and death data (days)", y = "Pearson's correlation", col = "NHS region") +
  theme(legend.position = "bottom") +
  guides(color = guide_legend(override.aes = list(fill = NA)))

cor_vs_lag_reg

5 Export data

We save the tables created during our analysis:


if (!dir.exists("excel_tables")) {
  dir.create("excel_tables")
}


## list all tables, and loop over export
tables_to_export <- c("r_all_sliding", "lag_cor")

for (e in tables_to_export) {
  rio::export(get(e),
              file.path("excel_tables",
                        paste0(e, ".xlsx")))
}

## also export result from regression on lagged data 
rio::export(lag_mod, file.path("excel_tables", "lag_mod.rds"))

6 System information

6.1 Outline

The following information documents the system on which the document was compiled.

6.2 System

This provides information on the operating system.

Sys.info()
##                                                                                            sysname 
##                                                                                           "Darwin" 
##                                                                                            release 
##                                                                                           "19.5.0" 
##                                                                                            version 
## "Darwin Kernel Version 19.5.0: Tue May 26 20:41:44 PDT 2020; root:xnu-6153.121.2~2/RELEASE_X86_64" 
##                                                                                           nodename 
##                                                                                   "Mac-1467.local" 
##                                                                                            machine 
##                                                                                           "x86_64" 
##                                                                                              login 
##                                                                                             "root" 
##                                                                                               user 
##                                                                                           "runner" 
##                                                                                     effective_user 
##                                                                                           "runner"

6.3 R environment

This provides information on the version of R used:

R.version
##                _                           
## platform       x86_64-apple-darwin15.6.0   
## arch           x86_64                      
## os             darwin15.6.0                
## system         x86_64, darwin15.6.0        
## status                                     
## major          3                           
## minor          6.3                         
## year           2020                        
## month          02                          
## day            29                          
## svn rev        77875                       
## language       R                           
## version.string R version 3.6.3 (2020-02-29)
## nickname       Holding the Windsock

6.4 R packages

This provides information on the packages used:

sessionInfo()
## R version 3.6.3 (2020-02-29)
## Platform: x86_64-apple-darwin15.6.0 (64-bit)
## Running under: macOS Catalina 10.15.5
## 
## Matrix products: default
## BLAS:   /Library/Frameworks/R.framework/Versions/3.6/Resources/lib/libRblas.0.dylib
## LAPACK: /Library/Frameworks/R.framework/Versions/3.6/Resources/lib/libRlapack.dylib
## 
## locale:
## [1] en_US.UTF-8/en_US.UTF-8/en_US.UTF-8/C/en_US.UTF-8/en_US.UTF-8
## 
## attached base packages:
## [1] stats     graphics  grDevices utils     datasets  methods   base     
## 
## other attached packages:
##  [1] ggnewscale_0.4.1     ggpubr_0.3.0         lubridate_1.7.9     
##  [4] chngpt_2020.5-21     cyphr_1.1.0          DT_0.13             
##  [7] kableExtra_1.1.0     janitor_2.0.1        remotes_2.1.1       
## [10] projections_0.4.1    earlyR_0.0.1         epitrix_0.2.2       
## [13] distcrete_1.0.3      incidence_1.7.1      rio_0.5.16          
## [16] reshape2_1.4.4       rvest_0.3.5          xml2_1.3.2          
## [19] linelist_0.0.40.9000 forcats_0.5.0        stringr_1.4.0       
## [22] dplyr_1.0.0          purrr_0.3.4          readr_1.3.1         
## [25] tidyr_1.1.0          tibble_3.0.1         ggplot2_3.3.2       
## [28] tidyverse_1.3.0      here_0.1             reportfactory_0.0.5 
## 
## loaded via a namespace (and not attached):
##  [1] colorspace_1.4-1  selectr_0.4-2     ggsignif_0.6.0    ellipsis_0.3.1   
##  [5] rprojroot_1.3-2   snakecase_0.11.0  fs_1.4.1          rstudioapi_0.11  
##  [9] farver_2.0.3      fansi_0.4.1       splines_3.6.3     knitr_1.28       
## [13] jsonlite_1.6.1    broom_0.5.6       dbplyr_1.4.4      compiler_3.6.3   
## [17] httr_1.4.1        backports_1.1.8   assertthat_0.2.1  Matrix_1.2-18    
## [21] cli_2.0.2         htmltools_0.5.0   prettyunits_1.1.1 tools_3.6.3      
## [25] gtable_0.3.0      glue_1.4.1        Rcpp_1.0.4.6      carData_3.0-4    
## [29] cellranger_1.1.0  vctrs_0.3.1       nlme_3.1-144      matchmaker_0.1.1 
## [33] crosstalk_1.1.0.1 xfun_0.14         ps_1.3.3          openxlsx_4.1.5   
## [37] lifecycle_0.2.0   rstatix_0.6.0     MASS_7.3-51.5     scales_1.1.1     
## [41] hms_0.5.3         sodium_1.1        yaml_2.2.1        curl_4.3         
## [45] gridExtra_2.3     stringi_1.4.6     kyotil_2019.11-22 boot_1.3-24      
## [49] pkgbuild_1.0.8    zip_2.0.4         rlang_0.4.6       pkgconfig_2.0.3  
## [53] evaluate_0.14     lattice_0.20-38   labeling_0.3      htmlwidgets_1.5.1
## [57] cowplot_1.0.0     processx_3.4.2    tidyselect_1.1.0  plyr_1.8.6       
## [61] magrittr_1.5      R6_2.4.1          generics_0.0.2    DBI_1.1.0        
## [65] pillar_1.4.4      haven_2.3.1       foreign_0.8-75    withr_2.2.0      
## [69] mgcv_1.8-31       survival_3.1-8    abind_1.4-5       modelr_0.1.8     
## [73] crayon_1.3.4      car_3.0-8         utf8_1.1.4        rmarkdown_2.3    
## [77] viridis_0.5.1     grid_3.6.3        readxl_1.3.1      data.table_1.12.8
## [81] blob_1.2.1        callr_3.4.3       reprex_0.3.0      digest_0.6.25    
## [85] webshot_0.5.2     munsell_0.5.0     viridisLite_0.3.0